An experimental investigation is conducted to study the flow patterns, spectral properties and energy fluxes in thin-layer turbulence with varying system sizes and damping rates. It is found that although a system-size vortex (an indicator of spectral condensation) occurs for small system sizes and does not for large ones, the spectra for different system sizes consistently exhibit a scaling close to $k^{-3}$ in inverse cascade (another indicator of spectral condensation). On the other hand, under a fixed system size larger than the friction-dominated length scale, the energy spectrum in the inverse cascade range changes from $k^{-3}$ to $k^{-5/3}$ as the damping rate increases, suggesting that the friction-dominated length scale may not be a suitable parameter for predicting spectral transition. At lower damping rates and large system sizes, turbulent structures grow larger via inverse cascade, manifesting as long streamers, and the small-scale vortices are suppressed. This suppression leads to a reduction of energy flux at intermediate scales and a change in the spectral shape. The dimensionless Taylor microscale is found to exhibit a monotonic dependence on the damping rate. With the reduction in the damping rate, the Taylor microscale increases to become comparable with the forcing scale, and the spectrum in inverse cascade transits to a steeper scaling, $k^{-3}$, indicating that the dimensionless Taylor microscale may be used as a diagnostic parameter for spectral transition.

This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil.

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in unsteady flows (e.g. Lagrangian particle tracking or ocean buoys), obtaining material measures of fluid rotation or stretching is an active topic of research. To facilitate frame-indifferent investigations in unsteady and sparsely sampled flows, we present a novel approach to quantify fluid stretching and rotation via relative Lagrangian velocities. This technique provides a formal objective extension of quasi-objective metrics to unsteady flows by accounting for mean flow behaviour. For extremely sparse experimental data, fluid structures may be significantly undersampled and the mean flow behaviour becomes difficult to quantify. We provide a means to maintain the accuracy of our novel sparse flow diagnostics in extremely sparse sampling scenarios, such as ocean buoy data and Lagrangian particle tracking. We use data from multiple numerical and experimental flows to show that our methods can identify structures beyond existing limits of sparse, frame-indifferent diagnostics and exhibit improved interpretability over common frame-dependent diagnostics.

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over-predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is presented which corrects this and is shown to conserve energy. New theoretical predictions are supported by numerical results which use averaging of simulations of wave scattering over finite sections of random bathymetry for which transfer matrix eigenvalues are used to accurately measure decay. The model of wave propagation used in this paper is derived from a linearised long-wavelength assumption whereby depth averaging leads to time harmonic waves being represented as solutions to a simple ordinary differential equation. In this paper it is shown how this can be adapted to incorporate a model of a continuous covering of the surface by fragmented floating ice. Attenuation of waves through broken ice of random thickness is then analysed in a similar manner as bed variations have been previously. General features of the predicted attenuation are discussed in relation to existing theoretical models for attenuation due to multiple scattering through random ice environments and to field data, particularly in the model's ability to capture a ‘rollover effect’ at higher frequencies.

The volume filtering of the governing equations of a particle-laden flow allows for simulating the fluid phase as a continuum, and accounting for the momentum exchange between the fluid and the particles by adding a source term in the fluid momentum equations. The volume filtering of the Navier–Stokes equations allows consideration of the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. It is common to either neglect these closures or model them using assumptions of which the implications are unclear. In the present paper, we carefully study every closure in the volume-filtered fluid momentum equation and investigate their impact on the momentum and energy transfer dependent on the filtering characteristics. We provide an analytical expression for the viscous closure that arises because the filter and spatial derivative in the viscous term do not commute. An analytical expression for the regularization of the particle momentum source of a single sphere in the Stokes regime is derived. Furthermore, we propose a model for the subfilter stress tensor, which originates from filtering the advective term. The model for the subfilter stress tensor is shown to agree well with the subfilter stress tensor for small filter widths relative to the size of the particle. We show that, in contrast to common practice, the subfilter stress tensor requires modelling and should not be neglected. For filter widths comparable to the particle size, we find that the commonly applied Gaussian regularization of the particle momentum source is a poor approximation of the spatial distribution of the particle momentum source, but for larger filter widths, the spatial distribution approaches a Gaussian. Furthermore, we propose a modified advective term in the volume-filtered momentum equation that consistently circumvents the common stability issues observed at locally small fluid volume fractions. Finally, we propose a generally applicable form of the volume-filtered momentum equation and its closures based on clear and well-founded assumptions. Based on the new findings, guidelines for point-particle simulations and the filter width with respect to the particle size and fluid mesh spacing are proposed.

The Whitham equation is a non-local, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at fixed spatial locations. To directly model data of this type, it is desirable to have equations that model the spatial evolution of time series. The spatial Whitham (sWhitham) equation, proposed as the spatial generalization of the Whitham equation, fills this need. In this paper, we study this equation and apply it to water-wave experiments on shallow and deep water. We compute periodic travelling-wave solutions to the sWhitham equation and examine their properties, including their stability. Results for small-amplitude solutions align with known results for the Whitham equation. This suggests that the systems are consistent in the weakly nonlinear regime. At larger amplitudes, there are some discrepancies. Notably, the sWhitham equation does not appear to admit cusped solutions of maximal wave height. In the second part, we compare predictions from the temporal and spatial Korteweg–de Vries and Whitham equations with measurements from laboratory experiments. We show that the sWhitham equation accurately models measurements of tsunami-like waves of depression, waves of elevation, and solitary waves on shallow water. Its predictions also compare favourably with experimental measurements of waves of depression and elevation on deep water. Accuracy is increased by adding a phenomenological damping term. Finally, we show that neither the sWhitham nor the temporal Whitham equation accurately models the evolution of wave packets on deep water.

Small heavy particles cannot be attracted into a region of closed streamlines in a non-accelerating frame (Sapsis & Haller, Chaos, vol. 20, issue 1, 2010, 017515). In a rotating system of vortices, however, particles can get trapped (Angilella, Physica D, vol. 239, issue 18, 2010, pp. 1789–1797) in the vicinity of vortices. We perform numerical simulations to examine trapping of inertial particles in a prototypical rotating flow described by a rotating pair of Lamb–Oseen vortices of identical strength, in the absence of gravity. Our parameter space includes the particle Stokes number $St$, which is a measure of the particle's inertia, and a density parameter $R$, which measures the particle's density relative to the fluid. In particular, we study the regime $0< R<1$ and $0< St<1$, which corresponds to an inertial particle that is finitely denser than the fluid. We show that in this regime, a significant fraction of particles can be trapped indefinitely close to the vortices, and display extreme clustering into objects of smaller dimension: attracting fixed points and limit cycles of different periods including chaotic attractors. As $St$ increases for a given $R$, we may have an incomplete or complete period-doubling route to chaos, as well as an unusual period-halving route back to a fixed point attractor. The fraction of trapped particles can be a non-monotonic function of $St$, and we may even have windows in $St$ for which no particle trapping occurs. At $St$ larger than a critical value, beyond which trapping ceases to exist, significant fractions of particles can spend long but finite times in the vortex vicinity. The inclusion of the Basset–Boussinesq history (BBH) force is imperative in our study due to the finite density of the particle. We observe that the BBH force significantly increases the basin of attraction over which trapping occurs, and also widens the range of $St$ for which trapping can be realised. Extreme clustering can be of significance in a host of physical applications, including planetesimal formation by aggregation of dust in protoplanetary discs, and aggregation of phytoplankton in the ocean. Our findings in the prototypical model provide impetus to conduct experiments and further numerical investigations to understand clustering of inertial particles.

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers ($Re_\tau =180, 550, 1000, 2000$ and $5200$). Employing the Karhunen–Loève decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and $Re_{\tau }$. With increasing $Re_{\tau }$, two distinct classes of structures become more energetic, namely wall-attached and detached eddies. The Voronoi methodology is shown to delineate these two classes without the need for specific criteria or thresholds. At the highest $Re_{\tau }$, the attached eddies scale linearly with the wall-normal distance with a slope of approximately $l_y\sim 1.2y/R$, while the detached eddies remain constant at the size of $l_y \approx 0.26R$, with a progressive shift towards the pipe centre. We extract these two classes of structures and describe their spatial characteristics, including radial size, helix angle and azimuthal self-similarity. The spatial distribution could help explain the differences in mean velocity between pipe and channel flows, as well as in modelling large and very-large-scale motions (LSM and VLSM). In addition, a comprehensive description is provided for both wall-attached and detached structures in terms of LSM and VLSM.

When subjected to external stress exceeding their yield stress ($\sigma _{Y}$), yield stress fluids (YSFs) undergo transition from solid to liquid. While the flow dynamics of capillary flows – including wetting, coating, spreading, and wicking – can be predicted accurately for fluids without yield stress, only a few asymptotic solutions have been validated against experiments for YSFs. In this study, we explore experimentally and theoretically the entire dynamics and solidifying process during capillary imbibition of YSFs, representing the fundamental aspect of capillarity-driven flow. We observe that during the gradual deceleration of capillary rise, YSFs exhibit apparent flow below $\sigma _{Y}$. This unexpected behaviour is linked to wall slip, manifested as plug flow in particle image velocimetry analyses. We introduce a model with numerical solutions, grounded in the rheological properties of YSFs and slip mechanisms, to accurately describe this liquid–solid transitional behaviour.

We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh–Bénard convection for the Rayleigh-number range $10^5\leq Ra \leq 10^{11}$ and $Pr=0.7$. Using a Cartesian slab with horizontal periodic boundary conditions and an aspect ratio of 4, we obtain statistical homogeneity in the horizontal $x$- and $y$-directions, thus approximating best an extended convection layer relevant for most geo- and astrophysical flow applications. We observe upon canonical use of combined long-time and area averages, with averaging periods of at least 100 free-fall times, that a global coherent mean flow is practically absent and that the magnitude of the velocity fluctuations is larger than the mean by up to 2 orders of magnitude. The velocity field close to the wall is a collection of differently oriented local shear-dominated flow patches interspersed by extensive shear-free incoherent regions which can be as large as the whole cross-section, unlike for a closed cylindrical convection cell of aspect ratio of the order 1. The incoherent regions occupy a 60 % area fraction for all Rayleigh numbers investigated here. Rather than resulting in a pronounced mean flow with small fluctuations about such a mean, as found in small-aspect-ratio convection, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport.